Heat and Thermodynamics 4 Question 15
17. The mass of a hydrogen molecule is $3.32 \times 10^{-27} kg$. If $10^{23}$ hydrogen molecules strike per second, a fixed wall of area 2 $cm^{2}$ at an angle of $45^{\circ}$ to the normal and rebound elastically with a speed of $10^{3} m / s$, then the pressure on the wall is nearly
(a) $2.35 \times 10^{4} N / m^{2}$
(b) $2.35 \times 10^{3} N / m^{2}$
(c) $4.70 \times 10^{2} N / m^{2}$
(d) $2.35 \times 10^{2} N / m^{2}$
(2018 Main)
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Solution:
- Pressure $=\frac{\text { Force }}{\text { Area }}$
$$ \begin{aligned} & =\frac{\frac{\text { Number of Collisions }}{sec} \times \frac{\text { Change in momentum }}{\text { collision }}}{\text { Area }} \\ & =\frac{10^{23} \times 2 m v \cos 45^{\circ}}{2 \times 10^{-4}}=2.35 \times 10^{3} N / m^{2} \end{aligned} $$
